Let f(z) = u(x,y) + i v(x,y) be an analytic function with z = x + iy and i = v-1. Given u(x,y) = xy a. Find v(x,y).Assume any integration constant to be zero. b. Express f(z) in terms of z and its complex conjugate z.

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter3: Functions And Graphs
Section3.3: Lines
Problem 21E
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1) Let f(z) = u(x.y) + i v(x,y) be an analytic function with z = x + i y and
i = v-1. Given u(x,y) = xy
a. Find v(x,y).Assume any integration constant to be zero.
b. Express f(z) in terms of z and its complex conjugate z.
Transcribed Image Text:1) Let f(z) = u(x.y) + i v(x,y) be an analytic function with z = x + i y and i = v-1. Given u(x,y) = xy a. Find v(x,y).Assume any integration constant to be zero. b. Express f(z) in terms of z and its complex conjugate z.
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